What is the integral of 25xe^{5x} ?

The integral of 25xe^{5x} is 5e^{5x}x-e^{5x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 25xe^{5x}

\int 25 x e^{5 x} d x

5 e^{5 x} x - e^{5 x} + C

Solution steps

\int 25 x e^{5 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 25 \cdot \int x e^{5 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{25} d u

= 25 \cdot \int \frac{e ^{u} u}{25} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 25 \cdot \frac{1}{25} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= 25 \cdot \frac{1}{25} (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= 25 \cdot \frac{1}{25} (e^{u} u - e^{u})

Substitute back

u = 5 x

= 25 \cdot \frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x})

Simplify

25 \cdot \frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x}) : 5 e^{5 x} x - e^{5 x}

= 5 e^{5 x} x - e^{5 x}

Add a constant to the solution

= 5 e^{5 x} x - e^{5 x} + C

\int \frac{4 x}{e ^{3 x}} d x

(0.3) (4)

\frac{d}{d x} (\frac{x ^{2} + x + 1}{x ^{\frac{3}{2}}})

(- 4, - 3), (3, - 3)

\int \frac{sin ( x )}{cos ( x )} d x

What is the integral of 25xe^{5x} ?
The integral of 25xe^{5x} is 5e^{5x}x-e^{5x}+C